**Evangelos Bartzos (University of Athens) **

*Algebraic and combinatorial methods for bounding the number of the complex embeddings of minimally rigid graphs *Bartzos

We are proposing methods to compute multihomogeneous Bezout bounds (m-Bezout) for counting the number of embeddings of minimally rigid graphs in $\CC^2$ (Laman graphs), $S^2$ and $\CC^3$ (Geiringer graphs) and we also examine their combinatorial aspects. We note that the bounds for Laman graphs in $\CC^2$ coincide with the bounds of their spherical embeddings in $S^2$. We also present computations that indicate that these bounds are tight for certain classes of graphs.

This is joint work with I.Z. Emiris and J. Schicho.